Definition 1.8 (see [1]}) 
Given a chief factor \(H/K\)  of a group \(G\) , the primitive group
\([H/K]*G\)  associated with \(H/K\)  in \(G\) coincides with the
semidirect product \([H/K]\bigl (G/{\operatorname{C}_G(H/K)}\bigr )\)  if \(H/K\)  is
abelian and with the quotient group \(G/{\operatorname{C}_G(H/K)}\)  if \(H/K\)  is
non-abelian.

